Question: Simplify. Multiply and remove all perfect squares from inside the square roots. Assume $b$ is positive. $2\sqrt{8b^3}\cdot 9\sqrt{18b}=$
Answer: Let's start by multiplying the factors within and without the square roots: $\begin{aligned} 2\sqrt{8b^3}\cdot 9\sqrt{18b} &=2\cdot 9\cdot\sqrt{8b^3}\cdot\sqrt{18b} \\\\ &=18\sqrt{144b^4} \end{aligned}$ Now we remove all perfect squares from inside the square root: $\begin{aligned} 18\sqrt{144b^4}&=18\sqrt{12^2\cdot \left(b^2\right)^2} \\\\ &=18\sqrt{12^2}\cdot\sqrt{\left(b^2\right)^2} \\\\ &=18\cdot 12\cdot b^2 \\\\ &=216b^2 \end{aligned}$ In conclusion, $2\sqrt{8b^3}\cdot 9\sqrt{18b}=216b^2$